Characterization of Foam Flowing in a Granular Medium in Presence of Oil by Small Angle Neutron Scattering

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Characterization of Foam Flowing in a Granular Medium

in Presence of Oil by Small Angle Neutron Scattering

Raphael Poryles, Thibaud Chevalier, Nicolas Gland, Elisabeth Rosenberg,

Loïc Barré

To cite this version:

Jour

nal

Name

Characterization of Foam Flowing in a Granular

Medium in Presence of Oil by Small Angle Neutron

Scattering

Raphaël Poryles,∗aThibaud Chevalier,a_{Nicolas Gland,}a_{Elisabeth Rosenberg}a_{and Loïc} Barré∗a

We present an experimental study of foam flow characterization inside a 3D granular medium packed in a cell. The foam is formed by coinjecting a surfactant solution and gas inside a cell filled with silica grains. The porous medium is initially saturated with dodecane and water before the gas-surfactant coinjection. To simplify the interpretation of the measurements, a contrast matching methodology has been applied in order to obtain a two phases system regarding the scattering length density values. The combination of transmission and incoherent scattering allow us to estimate the volume fractions of each phase whereas the coherent scattering is used to estimate the surface to volume ratio S/V related to water-oil and water-gas interfaces. Considering the evolution of S/V ratio, volume fractions and pressure difference, we infer some mechanisms of foam generation and transportation as well as oil removal.

1

Introduction

Foam injection in a porous medium is used in various industrial applications such as soil remediation1,2 _{and oil extraction}3_{. In}

oil industry, one challenge is to maximize the efficiency of the ex-traction. Typical oil fields production follows three stages. First a primary recovery simply relying on the natural pressure in the reservoir4. This is followed by a secondary recovery, by injection of a liquid to push the oil towards extraction wells. The resid-ual oil saturation (SOR) after this secondary stage is about 60 %5

and the tertiary stage also called Enhanced Oil Recovery (EOR) implements various methods (chemical, thermical, gas injection) to increase the oil production and optimize the sweeping of the reservoir4,6_{. One of the methods considered is foam injection}7_as

it decreases negative effects observed in the secondary oil recov-ery among which viscous fingering8. Understanding the dynam-ics of foam flowing in a porous medium is necessary to improve such technology.

Foam can be directly generated by coinjection of a gas and a surfactant solution in a porous medium9. The mechanisms of foam formation at the pore scale can be declined in three types: snap-off, leave behind and lamellae division10. When the foam is generated, an important increase of the pressure gradient is ob-served, resulting from the increase of effective gas viscosity and

a_{IFP Energies nouvelles, 1 et 4 avenue de Bois-Préau, 92852 Rueil-Malmaison, France} ∗ _{E-mail: [email protected] and [email protected]}

the decrease of relative permeability leading to a reduced mo-bility factor8,11,12. Many studies have been performed in quasi 2D Hele-Shaw cells and micromodels to observe the dynamics of the foam flow at the bubble scale13–20. Those experiments have shown many results including that bubbles can be trapped inside a single pore and that fragmentation and coalescence processes can occur. In 3D systems, the measurements are more compli-cated, since direct visualization is not possible. Some studies us-ing computational tomography (CT scan) provided a good imag-ing of the foam generation in porous media, and a direct correla-tion between the pressure increase and the foam developping in the medium but the limited spatial resolution does not give access to the pore and lamellae scales8,21–26_.

One important issue for applications in oil industry is the effect of oil on the stability of the foam. In the presence of oil, the foam flow can be highly modified, and its relative viscosity decreased, leading to a decrease in efficiency23,27–32.

By measuring neutron transmission and scattering and apply-ing a phase contrast matchapply-ing, we discuss the impact of oil on the foam formation inside the granular medium, and we access the different stages of oil transportation.

2

Experimental setup

2.1 Experimental setup

The experimental setup41_{is presented in Figure 1. The porous}

medium is contained in a silica cylindrical horizontal cell with a length l =7 cm and internal diameter d =4.2 mm. The cell is filled with hydrophilic silica grains, that were crushed and sieved at a size of 112-150 µm. By differential mass measurement of the cell, we measure a porosity of φ = 40 %.

The outlet of the cell is connected to two 1 liter buffer bottles. Pressure in the buffer bottles is controlled using a back pressure regulator (Brooks, SLA5820B). This sets the pressure at the out-let of the cell. The produced fluids are collected after the back pressure regulator.

The different fluids coinjected at the inlet of the cell are the following: first an aqueous solution of SDS (Sodium Dodecyl Sul-fate) at 2 g/L, and NaCl at 5 g/L. This solution is injected using a Vindum Pump (VP-12K). This concentration of SDS ensures that we are over the critical micellar concentration (CMC≈ 1 g/L) and provides an important foamability, but is diluted enough to en-sure a minimal number of micelles and consequently a low scat-tering contribution of the micelles in the scatscat-tering signal42. The second fluid is nitrogen gas (N2), stored in a compressed bottle,

and injected using a mass flow controller (Brooks, SLA5850S). A third injection is performed using a Pharmacia pump (P-500). This pump is used to inject the reference fluids and prepare the initial state. Those fluids are a 5 g/L NaCl water solution, and pure dodecane oil.

Pressure measurements are performed at the inlet and outlet of the cell, using absolute pressure sensors (Keller, PA-33X), from which we compute the differential pressure in the cell ∆P. 2.2 Experimental protocol

The goal of this experiment is to observe the influence of oil pres-ence in the porous media. The cell is first completely saturated with the NaCl solution. Dodecane is then injected at a flow rate of 20 mL per hour during one hour. After this injection, the cell is in an irreducible water saturation state (SWI). We then inject

a NaCl solution at the same flow rate (20 mL per hour) for one hour in order to reach the residual oil saturation (SOR). At this

state, the oil is under the form of clusters or blobs dispersed in the pore network mainly saturated with brine.

To produce foam inside the porous medium, we directly coin-ject the SDS surfactant solution, and the nitrogen gas inside the cell at the SORstate. The surfactant solution is injected at a flow

rate of 4.5 mL/hr, and the gas is injected at a rate of 5.5mL/hr at 5 bars, which is the back pressure at the outlet of the cell. This gives a fractional gas flow rate of 55 %, also called foam quality43.

The differential pressure ∆P is acquired every second of the experiment, which lasts for 14.5×104_{s (about 40 hours).}

During the experiment, neutron transmission and scattering

are measured. The details on the neutron acquisition are pre-sented in the following section.

2.3 SANS acquisition

The neutron line used is PA-20 of Orphée reactor at Laboratoire Léon Brillouin (LLB), Saclay (France).

The acquisitions are performed by measuring the neutron transmitted and scattered by the medium. A parallel neutron beam, 4 mm in diameter, crosses the cell at the middle of the granular medium. The neutron wavelength is selected at λ = 4 Å. The detector is placed at two different distances from the sample (2 m and 12 m), to capture two different range of wave vectors. At very small angles (12 m), the wave vector measured ranges from q = 0.004 to q = 0.071 Å−1and at small angles (2 m) from q= 0.022to q = 0.449 Å−1. The two ranges overlap, so we can reconstruct the entire scattering spectrum between q = 0.004 and q= 0.449Å−1_{. The acquisition time is 15 minutes for each}

config-uration. 2D isotropic raw intensities are converted to scattering differential section per unit volume I(q) (cm−1) following a stan-dard procedure33.

Additionally, we measure the transmission of the sample during two minutes with the detector at 12 m. The value of the trans-mission Tr is the total neutron flux measured crossing the cell ϕt

during two minutes divided by the incident flux ϕi: Tr = ϕt/ϕi.

This transmission corresponds to the neutrons not absorbed by the sample (scattered and non-scattered), and mainly depends on the quantity of oil and water in the cell.

To simplify the analysis, we used contrast matched solutions. The matching is performed using mixtures of deuterated and hy-drogenated products39,44. We choose to match the scattering length density (SLD) of the water phases (NaCl solution and surfactant solution) to the granular medium, and the dodecane SLD to the N2 gas one. Figure 2 gives the different scattering

length densities of the products, calculated from atomic scatter-ing lengths45and the corresponding matching. The water used to match the silica (SLD=3.475 × 1010_cm−2_{) is a mixture of 40 %}

of H2O and 60 % of D2O in mass. The oil is matched with the

N2 gas (SLD≈ 0) with a mixture containing 89 % of C12H26and

11 % of C12D26 in mass. Using this matching, we are able to

ob-tain contrast between the silica + water phases and the gas + oil phases. This contrast matching of four different phases two by two is uncommon and remain sparse in the literature.

We first perform three references measurement: the dry gran-ular medium, the water saturated medium, and the oil saturated medium. Transmission results are presented in Table 1. Figure 3 represents the scattering intensity measured I(q) as a function of the wave vector q for the three references. The different refer-ences are for the medium in a dry [◦], water saturated [] and oil saturated states [×].

Porous Medium DP Buffer bottles + BPR (5 bars) Effluents Pharmacia Pump Mass Flow Controller Vindum Pump N₂ Water, SDS + NaCl Water, NaCl Dodecane l=7 cm ` I₀ l d=4.2 mm 2 or 12 m (a) (b) I_t l I(q) Poro us m ediu m i

j

l

j

l

Fig. 1 (a) Experimental setup. The differential pressure ∆P is obtained from the pressure measured at the inlet and outlet of the cell. The reference NaCl solution and the dodecane is injected using a Pharmacia pump. The foam is created by coinjecting N2gas and a surfactant solution (SDS). A back pressure regulator sets the outlet pressure at 5 bar. (b) Schematic presentation of the neutron scattering line. The incident beam has a wavelength λ of 4 Å and a intensity Ii. The detector is placed at 2 or 12 m from the cell. The measured intensity on the detector is I(q) and depends on the wave vector q.

S

L

D

(

10

c

m

)

Silica

N

D

0

H

0

C

D

C

H

0

3.47

-0.46

-0.56

6.39

6.70

Fig. 2 Schematic view of the contrast matching. The water phase is matched with the silica (SLD=3.475 × 1010 _cm−2_{) and the oil phase is} matched with the N2 gas (SLD≈0). The percentage are expressed in mass.

foam35,38_as:

I(q) = A/q4+ B (1)

The continuous line on Figure 3 shows the adjustment at low q: I(q) ∼ A.q−4and at high q: I(q) ∼ B.

By using a regression at low angles, we can define the ratio of the surface area over the total volume S/V34as:

S/V = A/(2π∆SLD2) (2) where ∆SLD is the difference in the scattering length between the different phases (in our case, the grains/water, and the gas/oil). The values of the plateau B and the surface/volume ratio, for the different references are presented in Table 1.

We observe that the water and silica are correctly matched, since the coherent intensity scattered at low angles is very small (Figure 3 [], S/V in Table 1). For a similar reason, the oil and gas phases are also well matched, their intensity scattered at low angle is almost the same (Figure 3 [◦,×], S/V in Table 1). The observed differences gives a rough idea on error bars.

The value of the incoherent plateau B is given in Table 1. Since the incoherent scattering length of Si and O is null, the incoher-ent intensity is only related to hydrogen contincoher-ent (i.e oil and

wa-ter). According to their composition, the various phases ranks as follows: Bo> Bw> Bg. In the following, the indexes w, o, g will

correspond to the water, the oil and the gas phases respectively. Figure 4 presents the intensity I(q), in the cases of the initial state preparation: the irreducible water saturation state (SWI,

[◦]) and the residual oil state (SOR, [×]). The preparation of

these states are presented in the previous section. The values of transmission Tr, ratio S/V , and incoherent plateau B are pre-sented in Table 1. We observe that BSW I> BSORand (S/V )SW I>

(S/V )SOR, which is coherent with the fact that the SWIstate

con-tains more oil than the SORstate. Note that the grains are

hy-drophilic and are always covered with water (there is no oil-grains interfaces, except for the reference oil sample).

To estimate the saturation of the water phase Φw and the oil

phase Φo, we write the value of the measured plateau B as:

B= Bw.Φw+ Bo.Φo (3)

where Bw,ois the value for the references.

By having Φw+ Φo= 1, and solving the system, we have ΦSW Iw =

0.45, ΦSOR

w = 0.82, so ΦSW Io = 0.55, ΦSORo = 0.18.

Once we reach the SORstate, the coinjection of gas and

sur-factant solution is started, to generate the foam inside the porous medium.

Table 1 Reference values for the transmission Tr, the ratio S/V , and the incoherent plateau B

Dry Water Oil SWI SOR

Tr 0.87 0.58 0.39 0.45 0.57

S/V (cm−1) 619 5 636 267 149

B(cm−1) 0.001 0.020 0.065 0.045 0.028

3

Observations and analysis

3.1 Pressure evolution

10-2 10-1

q (Å

)

I

(cm

)

Fig. 3 Intensity I(q) as a function of the wave vector q for the three references. [◦: Dry medium], [×: Oil saturated], [: Water saturated]. The solid lines represent the adjustment in I ∼ q−4_{and I = B.}

10-2 10-1

q (Å

)

I

(cm

)

Fig. 4 Reference for the initial SWI state [◦] and the SORstate[×]. The solid lines represent the adjustment in I ∼ q−4_{and I = cst.}

outlet of the cell we only observe a succession of liquid and gas phase. The pressure slowly increases until t ≈ 9 × 104_{s (stage II),}

and then rapidly increases up to a pressure ∆P = 3.5 bars during stage III. At this point, we observe a well formed foam at the out-let of the cell. A second jump is observed, and the differential pressure finally stabilizes at ∆P ≈ 4.5 bars (stage IV). Preliminary tests (without neutron scattering) only showed one jump, with the same final value (∆P ≈ 4.5 bars). Therefore the second jump remains to be explained.

The ◦ symbols represent the times when neutron scattering has been measured. Since each acquisition lasts for 45 minutes, the points are represented at the half time of each measurement.

The three colored dots correspond to three examples shown in the following subsection.

0 5 10 15

t

_(s)

P

(bar)

IV

III

II

I

Fig. 5 differential pressure ∆P as a function of time t. The circles repre-sent the times when neutron scattering are measured. The three colored points correspond to the examples given in Figure 6.

3.2 Scattering spectrum

During the gas injection, we acquired data at two different config-urations. First we acquired during two minutes the transmission Trwith the detector placed at 12 m of the sample. After this first acquisition, we measure the neutron scattering of the sample (low q), with the detector at 12 m. The detector is then positioned at 2 m from the sample and scattering is again measured (high q). Finally, the detector is brought back to 12 m and the measure-ment cycle starts again. This process lasts for about 45 minutes, which includes the time to change the detector positions. Each configuration has been presented in Section 2.2.

Figure 6 shows three examples of neutron scattering spectrum I(q)corresponding to the colored dots on Figure 5: [×] at the beginning of injection when no foam is formed, [◦] at the pressure jump when foam starts to be created, [] when the the stationary regime is reached. The solid lines represent the adjustment in I(q) ∼ q−4and I(q) = cst (Equation 1). We measure the incoherent plateau B as well as the prefactor at low wave vectors A which gives us access to ratio S/V (Equation 2).

We see that for those particular cases, the prefactor A increases with time (so does the ratio S/V ), while the level of the plateau Bdecreases. This will be discussed in detail in the following sec-tions.

4

Results

4.1 Transmission

10-2 10-1

q (Å

)

I

(cm

)

Fig. 6 Intensity I(q) as a function of the wave vector q for three examples during the experiment. [×: beginning of injection] [◦: at the transition] [: in the stationary regime]. The solid lines represent the adjustment in I∼ q−4_{and I = cst.}

4.2 Incoherent plateau

At large q, the scattering intensity I(q) is constant (B in Equa-tion 1). Using a linear regression, we can access the value of this incoherent plateau for each acquisition (with the detector at 2 m). Figure 8 shows the value of this incoherent plateau as a function of time. The colored dots represent the examples given in Figure 6. We see that the evolution of the plateau is in oppo-sition with the pressure change. At the start of the experiment B≈ 0.027, and its value decreases slowly towards B ≈ 0.02 until foam starts forming, when its value drops to 0.005.

4.3 Phase saturation

Using the previous results on the transmission value Tr and the in-coherent plateau B, we get access to the saturation of each phase inside the porous matrix. We first write that the sum of the three phases volume fraction is equal to 1:

Φw+ Φg+ Φo= 1 (4)

where Φw, Φg and Φoare the volume fraction of water, gas and

oil phase in the porous volume.

Using the transmission measurement, we deduce the µ coeffi-cient given by Beer-Lambert law as:

µw,o= −ln(

Trw,o

Trdry

)/(d.φ ) (5)

where Trw,o is the transmission of the water and oil references

respectively, Trdry the dry reference, d the internal diameter of

the cell, and φ the porosity.

The value of the incoherent plateau B is given at each time by equation 3 in Section 2.3:

B= Bw.Φw+ Bo.Φo

with Bw,othe incoherent plateau for the references and Φw,othe

0

5

10

15

t

_(s)

₁₀

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

Tr

Fig. 7 Transmission coefficient Tr as a function of time t. The three colored points correspond to the examples given in Figure 6.

0 5 10 15

t

(s)

B

(cm

)

Fig. 8 Value of the incoherent plateau B (see Equation 1) as a function of time t. The three colored points correspond to the examples given in Figure 6.

percentage of water and oil phases in the porous volume (we as-sume that the incoherent plateau for the gas phase is negligible). In the same way, we can write down for the transmission mea-sured

− ln(Tr/Trdry)/d.φ = µw.Φw+ µo.Φo (6)

Writing down α = −ln(Tr/Trdry)/(d.φ ), and combining

Equa-tions 3 and 6, we can finally write for the three phases:

Φo= (α − (µw.B/Bw))/(µo− (µw.Bo/Bw)) (7)

Φw= (α − (µo.B/Bo))/(µw− (µo.Bw/Bo)) (8)

Φg= 1 − Φw− Φo (9)

0 5 10 15

t (s)

IV

III

II

I

Fig. 9 Phase proportions Φw,o,g, as a function of time. [: Water phase Φw] [×: Oil phase Φo] [◦: Gas phase Φg]. The four stage of foam forma-tion (I-IV) will be presented in Secforma-tion 5.

, [×, Φo] and [◦, Φg] as a function of time t. Considering that we

have three coupled equations, the solution presents strong fluc-tuations due to the computation and to the uncertainty of our measurements. We recall that B and Tr are acquired sequentially. Therefore, the error on fluids saturation is particularly important when these quantities vary strongly. This is illustrated during stage III when non physical (negative) values for Φo are

com-puted. During stage I, Φoslightly decreases. In stage II, Φgstarts

to increase due to the start of foam formation correlated to the increase of differential pressure ∆P in Figure 5. Then Φg jumps

up to 80% and Φwdrops (stage III). In stage IV the three different

phases saturations remain roughly constant. 4.4 Ratio S/V

By measuring the prefactor A at low angles scattering, we can get the ratio S/V (see Section 2.3). S/V is related to the scattering interfaces, oil/water and gas/water:

 S V  = S V  o−w + S V  g−w

For each contribution, S/V is related to the phase concentra-tion and the size of the scattering objects. For monodisperse and spherical objects of radius Rp and volume fraction φ , one can

write:  S V  = 3φ Rp  (10) Rpis also called the Porod radius34. In our case, for instance

in the water-oil interface, we have Ro−wp = (3.φ .Φo)/(S/V )o−w.

The evolution of this ratio with time is presented in Figure 10. Once again we find that this prefactor is correlated with the pres-sure variation, and thus the foam formation. This is an important result since it shows that the texture of the foam is continuously changing as the pressure gradient is increased. This ratio slightly decreases from 150 down to 100 cm−1(stage I), then it increases

back during stage II. In stage III it rises sharply up to 570 cm−1_.

Finally it slowly reduces down to 400 cm−1(stage IV).

0 5 10 15

t

_(s)

S/V

(cm

)

IV

III

II

I

Fig. 10 Ratio S/V (see Equation 1) as a function of time t. The three colored points correspond to the examples given in Figure 6. The four stages of foam formation (I-IV) will be discussed in detail Section 5.

5

Discussion

In this section we propose an interpretation of the four different stages (I-IV) identified on Figures 5,9 and 10.

During stage I, the differential pressure ∆P remains close to zero and no foam is formed. The gas follows preferential paths through the matrix which is confirmed by a low Φg. The main

contribution of the ratio S/V comes from the oil-water interface. Moreover this ratio S/V decreases slowly, as does the oil content Φo. Computing the equivalent Porod radius for the oil phase, we

obtain at the beginning of this first stage Ro−wp ≈ 16.0 µm and

at the end Ro−wp ≈ 15.6 µm. This shows that the oil blobs are

removed, without evolution of their average radius, from Φo≈

0.23to Φo≈ 0.13. With the same method, one can determine a

characteristical length of the porous medium from the dry state Rdryp ≈ 19.0 µm (S/V in Table 1), intermediate between the pore

and throat sizes. This would be in agreement with the oil blobs being localized inside the pores. In practice during this stage, the oil blob removal is induced by the presence of the surfactant which decreases the interfacial tension.

In stage II, a small increase of differential pressure ∆P, gas frac-tion Φg and ratio S/V is observed. This shows the beginning of

partial foam formation inside the porous medium. Since the oil follows the same trend as in stage I, we believe that the foam is created in the oil depleted zones, and the oil is still removed by surfactant action.

The beginning of stage III presents a sharp increase of differ-ential pressure ∆P, gas fraction Φg and ratio S/V as well as a

sharp decrease of Φw. The foam has then invaded most of the

(im-portant S/V and ∆P). Most of the remaining oil has been flushed outside of the porous medium by the foam invasion. Finally in stage IV the differential pressure and the phases concentration show an asymptotic behavior and tend to a constant value: the foam is in its completely structured form.

One interesting issue is the significant decrease of S/V in the stage III and IV. Since the pressure increases during this time, foam contribution can only lead to an increase of S/V ratio. Thus the oil-water interface evolution is the only possible reason for such evolution. This decrease being important (∼ 30% of the max-imum), and the oil being in small quantity (estimated as less than 2% of the volume), this remaining oil can only be present in the form of small droplets removed during this final stage. The S/V ratio tends to a asymptotic final value where we suppose that all the oil is removed (Φo= 0). From the S/V ratio decrease, from

564to 398 cm−1, one can estimate the maximum radius of the removed oil droplets as Ro−w

p < 1.4 µm. This is at least one order

of magnitude smaller than the initial oil blob size in stage I. We believe that this droplet transport is performed inside the foam plateau borders, nodes and the lamellae. These mechanisms have been reported in the literature46,47.

6

Conclusion

We present a new approach based on small angle neutron scat-tering to study foam transport in a representative 3D porous medium, in the presence of oil. This work is innovative in the technique used where four phases contrast matching has been performed: the SLD of water is matched to the silica grains one and the oil to the gas. It gives us access to a better spatial resolution compared to the usual measurements (CT-Scan and micro-models). By combining the transmission and the incoher-ent plateau, we estimated the three phases saturations in the porous volume. The strong added value is the measurement of the ratio S/V which gives us an information on the size of the scattering objects over a few order of magnitude. From this char-acterization we can infer the mechanisms of foam generation and transportation as well as oil removal. At the beginning of the coinjection, oil blobs are removed by the surfactant without sig-nificative variation of their size. The foam is first generated in the most permeable paths and area already swept by the surfactant. The foam then structures itself and invades the entire medium, flushing the residual oil. An interesting result is that, in the fi-nal stage, the oil transported by the foam is in a form of small droplets.

We believe that these results could open a more general us-age of neutron scattering for the study of foam flow especially in porous media, and this work shows the potentiality of it. The most striking contribution of such approach is to discriminate among the different mechanisms proposed in the literature for oil transportation by foam in a 3D representative porous medium. As a future work, to fully exploit neutron capabilities, one could explore more in details the scattering spectrum at intermediate wave vectors. This could give access to other information such as the shape, size and concentration of lamellae, oil droplets and

micelles. Another study axis would be to vary the injection condi-tions such as the flow rates, the surfactant nature or the salinity.

Acknowledgements

The neutron measurements have been performed on the PA-20 line at LLB Laboratory, CEA Saclay (France) under the project 910. We particularly thank for his help our local contact J. Jestin. The participants on the shifts were L. Barré, T. Chevalier, A. Fafet, N. Gland, P. Hayrault, F. Lutz, N. Pannacci, R. Poryles and E. Rosenberg (alphabetical order).

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